DPD Modelling of the Self- and Co-Assembly of Polymers and Polyelectrolytes in Aqueous Media: Impact on Polymer Science

This review article is addressed to a broad community of polymer scientists. We outline and analyse the fundamentals of the dissipative particle dynamics (DPD) simulation method from the point of view of polymer physics and review the articles on polymer systems published in approximately the last two decades, focusing on their impact on macromolecular science. Special attention is devoted to polymer and polyelectrolyte self- and co-assembly and self-organisation and to the problems connected with the implementation of explicit electrostatics in DPD numerical machinery. Critical analysis of the results of a number of successful DPD studies of complex polymer systems published recently documents the importance and suitability of this coarse-grained method for studying polymer systems.

Dissipative particle dynamics simulations in colloid and Interface science: a review

Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.

Effects of metal-polymer complexation on structure and transport properties of metal-substituted polyelectrolyte membranes

Morphological and transport properties of hydrated metal-substituted Nafion membranes doped with metal ions of different valency and coordination strength are explored using coarse-grained dissipative particle dynamics simulations. To incorporate the effects of metal-polymer complexation, we introduce a novel metal ion complexation model, in which the charged central metal ion is surrounded by dummy sites that coordinate with ligands. The model parameters are determined by matching the metal-ligand running coordination numbers and the diffusion coefficients obtained from atomistic simulations and/or experiments. The increase of valency and coordination strength is found to strongly influence both the morphology and transport characteristics of the membrane at all hydration levels. The membrane segregation into hydrophobic and hydrophilic sub-phases is affected by metal-sulphonate coordination induced crosslinking at the hydrophilic/hydrophobic interface. The simulation results indicate that the interfacial crosslinking influences the interfacial tension and thereby affect the growth and coalescence of water clusters upon the increase of hydration. Multivalent complexation hinders water and ion mobility and causes anomalous sub-diffusion and dramatic decrease of the water permeability and ionic conductivity. Our DPD model is found efficient in elucidating the mechanisms of coordination-induced cross-linking and complexation and predicting on a semi-quantitative level the morphological and transport properties of metal-substituted Nafion membranes depending on the ion valency and coordination strength. The proposed model can be further advanced and adopted for other polyelectrolyte systems, such as sulfonated block-copolymers, polysaccharide solutions and composites, and biopolymer assemblies.

Coacervate formation studied by explicit solvent coarse-grain molecular dynamics with the Martini model

Complex coacervates are liquid-liquid phase separated systems, typically containing oppositely charged polyelectrolytes. They are widely studied for their functional properties as well as their potential involvement in cellular compartmentalization as biomolecular condensates. Diffusion and partitioning of solutes into a coacervate phase are important to address because their highly dynamic nature is one of their most important functional characteristics in real-world systems, but are difficult to study experimentally or even theoretically without an explicit representation of every molecule in the system. Here, we present an explicit-solvent, molecular dynamics coarse-grain model of complex coacervates, based on the Martini 3.0 force field. We demonstrate the accuracy of the model by reproducing the salt dependent coacervation of poly-lysine and poly-glutamate systems, and show the potential of the model by simulating the partitioning of ions and small nucleotides between the condensate and surrounding solvent phase. Our model paves the way for simulating coacervates and biomolecular condensates in a wide range of conditions, with near-atomic resolution.

Solubilization of Charged Porphyrins in Interpolyelectrolyte Complexes: A Computer Study

Using coarse-grained dissipative particle dynamics (DPD) with explicit electrostatics, we performed (i) an extensive series of simulations of the electrostatic co-assembly of asymmetric oppositely charged copolymers composed of one (either positively or negatively charged) polyelectrolyte (PE) block A and one water-soluble block B and (ii) studied the solubilization of positively charged porphyrin derivatives (P+) in the interpolyelectrolyte complex (IPEC) cores of co-assembled nanoparticles. We studied the stoichiometric mixtures of 137 A10+B25 and 137 A10-B25 chains with moderately hydrophobic A blocks (DPD interaction parameter aAS=35) and hydrophilic B blocks (aBS=25) with 10 to 120 P+ added (aPS=39). The P+ interactions with other components were set to match literature information on their limited solubility and aggregation behavior. The study shows that the moderately soluble P+ molecules easily solubilize in IPEC cores, where they partly replace PE+ and electrostatically crosslink PE- blocks. As the large P+ rings are apt to aggregate, P+ molecules aggregate in IPEC cores. The aggregation, which starts at very low loadings, is promoted by increasing the number of P+ in the mixture. The positively charged copolymers repelled from the central part of IPEC core partially concentrate at the core-shell interface and partially escape into bulk solvent depending on the amount of P+ in the mixture and on their association number, AS. If AS is lower than the ensemble average ⟨AS⟩n, the copolymer chains released from IPEC preferentially concentrate at the core-shell interface, thus increasing AS, which approaches ⟨AS⟩n. If AS>⟨AS⟩n, they escape into the bulk solvent.

Computer study of the solubilization of polymer chains in polyelectrolyte complex cores of polymeric nanoparticles in aqueous media

The formation and structure of nanoparticles containing non-polar polymer chains solubilized in interpolyelectrolyte complex (IPC) cores and the partitioning of non-polar chains between bulk solvent and IPC cores were studied by coarse-grained computer simulations. The choice of the model system was inspired by experimental results published by van der Burgh et al. (Langmuir, 2004, 20, 1073-1084). The dissipative particle dynamics (DPD) simulations reproduced the structure and basic features of co-assembled nanoparticles described by experimentalists well at the semi-quantitative coarse-grained level and revealed new properties of co-assembled particles. The simulated co-assemblies were used as reference systems for the solubilization studies. Their results show that non-polar polymers (electrically neutral and compatible with core-forming chains) solubilize easily in IPC cores. They intermix with polyelectrolyte blocks in cores and do not hinder, but, on the contrary, they slightly promote the electrostatic co-assembly.

Structure and Dynamics of Stimuli-Responsive Nanoparticle Monolayers at Fluid Interfaces

Stimuli-responsive nanoparticles at fluid interfaces offer great potential for realizing on-demand and controllable self-assembly that can benefit various applications. Here, we conducted electrostatic dissipative particle dynamics simulations to provide a fundamental understanding of the microstructure and interfacial dynamics of responsive nanoparticle monolayers at a water-oil interface. The model nanoparticle is functionalized with polyelectrolytes to render the pH sensitivity, which permits further manipulation of the monolayer properties. The monolayer structure was analyzed in great detail through the density and electric field distributions, structure factor, and Voronoi tessellation. Even at a low surface coverage, a continuous disorder-to-order phase transition was observed when the particle's degree of ionization increases in response to pH changes. The six-neighbor particle fraction and bond orientation order parameter quantitatively characterize the structural transition induced by long-range electrostatic interactions. Adding salt can screen the electrostatic interactions and offer additional control on the monolayer structure. The detailed dynamics of the monolayer in different states was revealed by analyzing mean-squared displacements, in which different diffusion regimes were identified. The self-diffusion of individual particles and the collective dynamics of the whole monolayer were probed and correlated with the structural transition. Our results provide deeper insight into the dynamic behavior of responsive nanoparticle surfactants and lay the groundwork for bottom-up synthesis of novel nanomaterials, responsive emulsions, and microdroplet reactors.

Adsorption of amphiphilic graft copolymers in solvents selective for the grafts on a lyophobic surface: a coarse-grained simulation study

The sorption of graft copolymers on surfaces attractive only for the backbone and its effect on the conformational behavior of adsorbed/desorbed chains in solvents good for the grafts and poor for the backbone was studied by coarse-grained computer simulations.